"The Israeli army's leadership allowed the reopening of stores on Sahla Street, which runs from the area near the Ibrahimi mosque" through Hebron's old town, Dawud al-Zaatari told journalists.
"This is the first time the army has allowed these shops to open since the beginning of the second intifada" he added.
The IDF would also be easing movement restrictions ahead of the Muslim holy month of Ramadan, Zaatari said, by opening two roads south of the city which have been closed for years.
The IDF could not immediately confirm or deny the Palestinian mayor's statements.
The army closed more than 500 Hebron shops during the second intifada, most of them along the deserted Shuhada (martyrs) Street near the old town, according to a local planning official.